Question

what is the surface area of the cylinder with height 5 ft and radius 7 ft? round your answer to the nearest thousandth.

Explanation:

Step1: Recall total surface area formula

The total surface area of a cylinder is $SA = 2\pi r^2 + 2\pi r h$, where $r$ is radius, $h$ is height.

Step2: Substitute given values

Substitute $r=7$ ft, $h=5$ ft:
$SA = 2\pi (7)^2 + 2\pi (7)(5)$

Step3: Calculate each term

First term: $2\pi \times 49 = 98\pi$
Second term: $2\pi \times 35 = 70\pi$

Step4: Sum terms and compute value

$SA = 98\pi + 70\pi = 168\pi$
Calculate numerical value: $168 \times 3.1415926535 \approx 527.7875658$

Step5: Round to nearest thousandth

Round $527.7875658$ to 3 decimal places.

Answer:

527.788 square feet